Schedule:

We will meet until August 29, 2019, inclusive.

Huron Classroom Thursdays 4:00 – 6.00

1. I will try to discuss a backbone of the topics presented in the first five chapters of the book. Sometimes I will skip whole sections completely for the sake of time so that we can get an idea of what the topic is about. This is not so terrible since many results are familiar from other areas (i.e. several construction in Lie algebras) and we have many analogies with the known case of smooth manifolds.
2. I try to update this page frequently and upload the notes I use whenever I use them. Notice that my notes and my presentation may differ in order or content slightly, but if you miss one lecture and see what happens in the notes you will be fine next time regardless.
3. I am not an expert in this topic, I am learning as well so please tell me mistakes or comments or references I could add.
4. We begin at 4.10 but from 4:00 to 4.10 I talk about a “nice fact” of something wlse that I am reading, not necessarily of mathematics.

Bibliography:

 p -adic Lie Groups, Peter Schneider.

 Arithmetic Differential Operators over the p-adic Integers, Claire C. Ralph, Santiago R. Simanca

Mostly for comparison and review of topology:

 Introduction to Topological Manifolds, Second Edition, John M. Lee, Springer GTM 202

 Introduction to Smooth Manifolds, First Edition, John M. Lee, Springer GTM 218

Logbook:

Notes:

•  Section 1.2: In here the continuos dual space is defined. We skipped this section since we use our intuition of the archimedean case and change it as we need (we do this just for the sake of time!).
•  Section 1.3: Deals with convergence. In particular it proves the concept of conditional convergence doesn’t exist in this case.
• Inverse Function Theorem: Compare the proof of the inverse function theorem (, Proposition 4.3) based on  Lemma 4.2, with the classical case in , Theorem 7.6.
• Point of expansion: We did not prove Point of expansion ( Corollary 5.5) but the proof is instructive.
• Characteristic: So far, we have made no distinction by field characteristic but some theorems and results require it or have a different proof. See for example  Corollary 5.7, 5.8.
• Paracompactness: To review this concept see , chapter 4. For us  Lemma 4.80 and  Theorem 4.81 are the important ones. Notice that part of the proof of  Theorem 8.7 is exactly  Lemma 4.84. What makes the difference then in the proof is the third claim in (i) implies (ii).

Alternative References: